and x is the same for all equations you may estimate it equation by
equation
OLS (regress y1 x1 and so on) or you may run sureg. (Seemingly unrelated
regression model). In both cases, as long as x is the same for all
equations, you should get the same results. Check Greene, Econometric
Analysis, Ch. 14. for details.
If you have various x in the different equations you should apply sureg. As
long as the error terms are uncorrelated, you may also apply OLS. However,
this is written in detail in the Greene-Text-Book.